His career began at age 12 playing Craig Harris on the ITV soap opera Coronation Street from 2002 to 2006.

He went on to become an established West End and Broadway performer, starring in shows such as Legally Blonde (2010) and Ghost (2011–2012).

He appeared in the recurring role of Ken on Netflix's The Sandman in 2022, and has played Lt. James Brice on Syfy's The Ark since 2023.

His father was born in Glasgow, Scotland, [3] Fleeshman began his professional career in the film called An Angel for May.

Fleeshman later filmed an episode of Blue Murder in 2007 in which he played the character Ben Holroyd, starring alongside Jill Halfpenny.

On 16 June 2010, Fleeshman joined the company of Legally Blonde in London, taking over from Duncan James in the role of Warner.

In 2009, he played the role of a musically talented but troubled boy named Kyle Caddick in a six-part BBC drama series All the Small Things allowing him to act as well as sing.

The show premiered at the Opera House, Manchester on 28 March 2011 and moved to the Piccadilly Theatre on 22 June 2011.

In 2013, Fleeshman starred as Bobby Strong in the UK premiere of the hit satirical musical, Urinetown, directed by Jamie Lloyd, at the St James Theatre.

In 2018, Fleeshman took on the role of Air-Steward 'Andy' in the West-End gender swapped revival of Stephen Sondheim's Company, directed by Marianne Elliot.

[11] In 2019, Fleeshman announced via his Instagram account that he is now a vegetarian and had been meat-free for over two years at that point, having "never felt better ethically or physically".